Neutrino oscillations and big bang nucleosynthesis☆
Introduction
The implications of neutrino masses in cosmology and astrophysics are numerous. One fascinating effect, is that of relic neutrino asymmetries, which may be produced if there is mixing between active and sterile neutrino species [1].
Neutrino asymmetries are interesting since they affect big bang nucleosynthesis (BBN), altering the primordial helium yield. BBN is particularly sensitive to an asymmetry between the νe and . Additionally, since the matter potential arising from forward scattering is proportional to the asymmetry, a large asymmetry will suppress active-sterile oscillation modes which could otherwise equilibrate sterile neutrino species around the time of BBN.
Section snippets
Relic neutrino asymmetries
First consider two-flavour mixing between an active neutrino, να, and a sterile neutrino, νs. For each neutrino flavour we define an asymmetrywhere nν and nγ are the neutrino and photon number densities, respectively.
The neutrino momentum distributions, N(p), are such thatand in thermal equilibrium are just given by Fermi-Dirac distributionsHere T is the temperature and , with μ being the neutrino chemical potential. In equilibrium, Lα is
Big bang nucleosynthesis and a four neutrino model
We wish to determine the impact of such asymmetry production on the BBN light element abundances, and in particular, on the helium yield. In general, the results are somewhat model dependent (compare, say, [7] with [8].)
The results are particularly sensitive to the size of the νe asymmetry, which directly affects the neutron/proton ratio through the reaction ratesThe n/p ratio determines the helium mass fraction YP via the equation
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Invited talk at the NUFACT’01 workshop in Tsukuba, Japan, 24–30 May 2001.